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Again, in regard to the differentiae, we must examine in like manner whether the differentiae, too, that he has stated be those of the genus. For if a man has not defined the object by the differentiae peculiar to it, or has mentioned something such as is utterly incapable of being a differentia of anything, e.g. ‘animal’ or ‘substance’, clearly he has not defined it at all: for the aforesaid terms do not differentiate anything at all. Further, we must see whether the differentia stated possesses anything that is coordinate with it in a division; for, if not, clearly the one stated could not be a differentia of the genus. For a genus is always divided by differentiae that are co-ordinate members of a division, as, for instance, by the terms ‘walking’, ‘flying’, ‘aquatic’, and ‘biped’. Or see if, though the contrasted differentia exists, it yet is not true of the genus, for then, clearly, neither of them could be a differentia of the genus; for differentiae that are co-ordinates in a division with the differentia of a thing are all true of the genus to which the thing belongs. Likewise, also, see if, though it be true, yet the addition of it to the genus fails to make a species. For then, clearly, this could not be a specific differentia of the genus: for a specific differentia, if added to the genus, always makes a species. If, however, this be no true differentia, no more is the one adduced, seeing that it is a co-ordinate member of a division with this.
Moreover, see if he divides the genus by a negation, as those do who define line as ‘length without breadth’: for this means simply that it has not any breadth. The genus will then be found to partake of its own species: for, since of everything either an affirmation or its negation is true, length must always either lack breadth or possess it, so that ‘length’ as well, i.e. the genus of ‘line’, will be either with or without breadth. But
‘length without breadth’ is the definition of a species, as also is ‘length with breadth’: for ‘without breadth’ and ‘with breadth’ are differentiae, and the genus and differentia constitute the definition of the species.
Hence the genus would admit of the definition of its species. Likewise, also, it will admit of the definition of the differentia, seeing that one or the other of the aforesaid differentiae is of necessity predicated of the genus. The usefulness of this principle is found in meeting those who assert the existence of ‘Ideas’: for if absolute length exist, how will it be predicable of the genus that it has breadth or that it lacks it? For one assertion or the other will have to be true of ‘length’ universally, if it is to be true of the genus at all: and this is contrary to the fact: for there exist 319
both lengths which have, and lengths which have not, breadth. Hence the only people against whom the rule can be employed are those who assert that a genus is always numerically one; and this is what is done by those who assert the real existence of the ‘Ideas’; for they allege that absolute length and absolute animal are the genus.
It may be that in some cases the definer is obliged to employ a negation as well, e.g. in defining privations. For ‘blind’ means a thing which cannot see when its nature is to see. There is no difference between dividing the genus by a negation, and dividing it by such an affirmation as is bound to have a negation as its co-ordinate in a division, e.g. supposing he had defined something as ‘length possessed of breadth’; for co-ordinate in the division with that which is possessed of breadth is that which possesses no breadth and that only, so that again the genus is divided by a negation.
Again, see if he rendered the species as a differentia, as do those who define ‘contumely’ as ‘insolence accompanied by jeering’; for jeering is a kind of insolence, i.e. it is a species and not a differentia.
Moreover, see if he has stated the genus as the differentia, e.g. ‘Virtue is a good or noble state: for ‘good’ is the genus of ‘virtue’. Or possibly
‘good’ here is not the genus but the differentia, on the principle that the same thing cannot be in two genera of which neither contains the other: for ‘good’ does not include ‘state’, nor vice versa: for not every state is good nor every good a ‘state’. Both, then, could not be genera, and consequently, if ‘state’ is the genus of virtue, clearly ‘good’ cannot be its genus: it must rather be the differentia’. Moreover, ‘a state’ indicates the essence of virtue, whereas ‘good’ indicates not the essence but a quality: and to indicate a quality is generally held to be the function of the differentia. See, further, whether the differentia rendered indicates an individual rather than a quality: for the general view is that the differentia always expresses a quality.
Look and see, further, whether the differentia belongs only by accident to the object defined. For the differentia is never an accidental attribute, any more than the genus is: for the differentia of a thing cannot both belong and not belong to it.
Moreover, if either the differentia or the species, or any of the things which are under the species, is predicable of the genus, then he could not have defined the term. For none of the aforesaid can possibly be predicated of the genus, seeing that the genus is the term with the widest range of all. Again, see if the genus be predicated of the differentia; for the general view is that the genus is predicated, not of the differentia, but of the 320
objects of which the differentia is predicated. Animal (e.g.) is predicated of ‘man’ or ‘ox’ or other walking animals, not of the actual differentia itself which we predicate of the species. For if ‘animal’ is to be predicated of each of its differentiae, then ‘animal’ would be predicated of the species several times over; for the differentiae are predicates of the species.
Moreover, the differentiae will be all either species or individuals, if they are animals; for every animal is either a species or an individual.
Likewise you must inquire also if the species or any of the objects that come under it is predicated of the differentia: for this is impossible, seeing that the differentia is a term with a wider range than the various species. Moreover, if any of the species be predicated of it, the result will be that the differentia is a species: if, for instance, ‘man’ be predicated, the differentia is clearly the human race. Again, see if the differentia fails to be prior to the species: for the differentia ought to be posterior to the genus, but prior to the species.
Look and see also if the differentia mentioned belongs to a different genus, neither contained in nor containing the genus in question. For the general view is that the same differentia cannot be used of two non-subaltern genera. Else the result will be that the same species as well will be in two non-subaltern genera: for each of the differentiae imports its own genus, e.g. ‘walking’ and ‘biped’ import with them the genus ‘animal’. If, then, each of the genera as well is true of that of which the differentia is true, it clearly follows that the species must be in two non-subaltern genera. Or perhaps it is not impossible for the same differentia to be used of two non-subaltern genera, and we ought to add the words ‘except they both be subordinate members of the same genus’. Thus ‘walking animal’
and ‘flying animal’ are non-subaltern genera, and ‘biped’ is the differentia of both. The words ‘except they both be subordinate members of the same genus’ ought therefore to be added; for both these are subordinate to ‘animal’. From this possibility, that the same differentia may be used of two non-subaltern genera, it is clear also that there is no necessity for the differentia to carry with it the whole of the genus to which it belongs, but only the one or the other of its limbs together with the genera that are higher than this, as ‘biped’ carries with it either ‘flying’ or ‘walking animal’.
See, too, if he has rendered ‘existence in’ something as the differentia of a thing’s essence: for the general view is that locality cannot differentiate between one essence and another. Hence, too, people condemn those who divide animals by means of the terms ‘walking’ and ‘aquatic’, on the ground that ‘walking’ and ‘aquatic’ indicate mere locality. Or 321
possibly in this case the censure is undeserved; for ‘aquatic’ does not mean ‘in’ anything; nor does it denote a locality, but a certain quality: for even if the thing be on the dry land, still it is aquatic: and likewise a land-animal, even though it be in the water, will still be a and not an aquatic-animal. But all the same, if ever the differentia does denote existence in something, clearly he will have made a bad mistake.
Again, see if he has rendered an affection as the differentia: for every affection, if intensified, subverts the essence of the thing, while the differentia is not of that kind: for the differentia is generally considered rather to preserve that which it differentiates; and it is absolutely impossible for a thing to exist without its own special differentia: for if there be no
‘walking’, there will be no ‘man’. In fact, we may lay down absolutely that a thing cannot have as its differentia anything in respect of which it is subject to alteration: for all things of that kind, if intensified, destroy its essence. If, then, a man has rendered any differentia of this kind, he has made a mistake: for we undergo absolutely no alteration in respect of our differentiae.
Again, see if he has failed to render the differentia of a relative term relatively to something else; for the differentiae of relative terms are themselves relative, as in the case also of knowledge. This is classed as speculative, practical and productive; and each of these denotes a relation: for it speculates upon something, and produces something and does something.
Look and see also if the definer renders each relative term relatively to its natural purpose: for while in some cases the particular relative term can be used in relation to its natural purpose only and to nothing else, some can be used in relation to something else as well. Thus sight can only be used for seeing, but a strigil can also be used to dip up water.
Still, if any one were to define a strigil as an instrument for dipping water, he has made a mistake: for that is not its natural function. The definition of a thing’s natural function is ‘that for which it would be used by the prudent man, acting as such, and by the science that deals specially with that thing’.
Or see if, whenever a term happens to be used in a number of relations, he has failed to introduce it in its primary relation: e.g. by defining
‘wisdom’ as the virtue of ‘man’ or of the ‘soul,’ rather than of the
‘reasoning faculty’: for ‘wisdom’ is the virtue primarily of the reasoning faculty: for it is in virtue of this that both the man and his soul are said to be wise.
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Moreover, if the thing of which the term defined has been stated to be an affection or disposition, or whatever it may be, be unable to admit it, the definer has made a mistake. For every disposition and every affection is formed naturally in that of which it is an affection or disposition, as knowledge, too, is formed in the soul, being a disposition of soul. Sometimes, however, people make bad mistakes in matters of this sort, e.g.
all those who say that ‘sleep’ is a ‘failure of sensation’, or that
‘perplexity’ is a state of ‘equality between contrary reasonings’, or that
‘pain’ is a ‘violent disruption of parts that are naturally conjoined’. For sleep is not an attribute of sensation, whereas it ought to be, if it is a failure of sensation. Likewise, perplexity is not an attribute of opposite reasonings, nor pain of parts naturally conjoined: for then inanimate things will be in pain, since pain will be present in them. Similar in character, too, is the definition of ‘health’, say, as a ‘balance of hot and cold elements’: for then health will be necessarily exhibited by the hot and cold elements: for balance of anything is an attribute inherent in those things of which it is the balance, so that health would be an attribute of them.
Moreover, people who define in this way put effect for cause, or cause for effect. For the disruption of parts naturally conjoined is not pain, but only a cause of pain: nor again is a failure of sensation sleep, but the one is the cause of the other: for either we go to sleep because sensation fails, or sensation fails because we go to sleep. Likewise also an equality between contrary reasonings would be generally considered to be a cause of perplexity: for it is when we reflect on both sides of a question and find everything alike to be in keeping with either course that we are perplexed which of the two we are to do.
Moreover, with regard to all periods of time look and see whether there be any discrepancy between the differentia and the thing defined: e.g. supposing the ‘immortal’ to be defined as a ‘living thing immune at present from destruction’. For a living thing that is immune ‘at present’
from destruction will be immortal ‘at present’. Possibly, indeed, in this case this result does not follow, owing to the ambiguity of the words
‘immune at present from destruction’: for it may mean either that the thing has not been destroyed at present, or that it cannot be destroyed at present, or that at present it is such that it never can be destroyed.
Whenever, then, we say that a living thing is at present immune from destruction, we mean that it is at present a living thing of such a kind as never to be destroyed: and this is equivalent to saying that it is immortal, so that it is not meant that it is immortal only at present. Still, if ever it does happen that what has been rendered according to the definition 323
belongs in the present only or past, whereas what is meant by the word does not so belong, then the two could not be the same. So, then, this commonplace rule ought to be followed, as we have said.
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You should look and see also whether the term being defined is applied in consideration of something other than the definition rendered.
Suppose (e.g.) a definition of ‘justice’ as the ‘ability to distribute what is equal’. This would not be right, for ‘just’ describes rather the man who chooses, than the man who is able to distribute what is equal: so that justice could not be an ability to distribute what is equal: for then also the most just man would be the man with the most ability to distribute what is equal.
Moreover, see if the thing admits of degrees, whereas what is rendered according to the definition does not, or, vice versa, what is rendered according to the definition admits of degrees while the thing does not. For either both must admit them or else neither, if indeed what is rendered according to the definition is the same as the thing. Moreover, see if, while both of them admit of degrees, they yet do not both become greater together: e.g. suppose sexual love to be the desire for intercourse: for he who is more intensely in love has not a more intense desire for intercourse, so that both do not become intensified at once: they certainly should, however, had they been the same thing.
Moreover, suppose two things to be before you, see if the term to be defined applies more particularly to the one to which the content of the definition is less applicable. Take, for instance, the definition of ‘fire’ as the ‘body that consists of the most rarefied particles’. For ‘fire’ denotes flame rather than light, but flame is less the body that consists of the most rarefied particles than is light: whereas both ought to be more applicable to the same thing, if they had been the same. Again, see if the one expression applies alike to both the objects before you, while the other does not apply to both alike, but more particularly to one of them.
Moreover, see if he renders the definition relative to two things taken separately: thus, the beautiful’ is ‘what is pleasant to the eyes or to the ears”: or ‘the real’ is ‘what is capable of being acted upon or of acting’.
For then the same thing will be both beautiful and not beautiful, and likewise will be both real and not real. For ‘pleasant to the ears’ will be the same as ‘beautiful’, so that ‘not pleasant to the ears’ will be the same 324
as ‘not beautiful’: for of identical things the opposites, too, are identical, and the opposite of ‘beautiful’ is ‘not beautiful’, while of ‘pleasant to the ears’ the opposite is not pleasant to the cars’: clearly, then, ‘not pleasant to the ears’ is the same thing as ‘not beautiful’. If, therefore, something be pleasant to the eyes but not to the ears, it will be both beautiful and not beautiful. In like manner we shall show also that the same thing is both real and unreal.
Moreover, of both genera and differentiae and all the other terms rendered in definitions you should frame definitions in lieu of the terms, and then see if there be any discrepancy between them.
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If the term defined be relative, either in itself or in respect of its genus, see whether the definition fails to mention that to which the term, either in itself or in respect of its genus, is relative, e.g. if he has defined
‘knowledge’ as an ‘incontrovertible conception’ or ‘wishing’ as ‘painless conation’. For of everything relative the essence is relative to something else, seeing that the being of every relative term is identical with being in a certain relation to something. He ought, therefore, to have said that knowledge is ‘conception of a knowable’ and that wishing is ‘conation for a good’. Likewise, also, if he has defined ‘grammar’ as ‘knowledge of letters’: whereas in the definition there ought to be rendered either the thing to which the term itself is relative, or that, whatever it is, to which its genus is relative. Or see if a relative term has been described not in relation to its end, the end in anything being whatever is best in it or gives its purpose to the rest. Certainly it is what is best or final that should be stated, e.g. that desire is not for the pleasant but for pleasure: for this is our purpose in choosing what is pleasant as well.
Look and see also if that in relation to which he has rendered the term be a process or an activity: for nothing of that kind is an end, for the completion of the activity or process is the end rather than the process or activity itself. Or perhaps this rule is not true in all cases, for almost everybody prefers the present experience of pleasure to its cessation, so that they would count the activity as the end rather than its completion.
Again see in some cases if he has failed to distinguish the quantity or quality or place or other differentiae of an object; e.g. the quality and quantity of the honour the striving for which makes a man ambitious: for all men strive for honour, so that it is not enough to define the ambitious 325
man as him who strives for honour, but the aforesaid differentiae must be added. Likewise, also, in defining the covetous man the quantity of money he aims at, or in the case of the incontinent man the quality of the pleasures, should be stated. For it is not the man who gives way to any sort of pleasure whatever who is called incontinent, but only he who gives way to a certain kind of pleasure. Or again, people sometimes define night as a ‘shadow on the earth’, or an earthquake as a movement of the earth’, or a cloud as ‘condensation of the air’, or a wind as a
‘movement of the air’; whereas they ought to specify as well quantity, quality, place, and cause. Likewise, also, in other cases of the kind: for by omitting any differentiae whatever he fails to state the essence of the term. One should always attack deficiency. For a movement of the earth does not constitute an earthquake, nor a movement of the air a wind, irrespective of its manner and the amount involved.
Moreover, in the case of conations, and in any other cases where it applies, see if the word ‘apparent’ is left out, e.g. ‘wishing is a conation after the good’, or ‘desire is a conation after the pleasant’-instead of saying ‘the apparently good’, or ‘pleasant’. For often those who exhibit the conation do not perceive what is good or pleasant, so that their aim need not be really good or pleasant, but only apparently so. They ought, therefore, to have rendered the definition also accordingly. On the other hand, any one who maintains the existence of Ideas ought to be brought face to face with his Ideas, even though he does render the word in question: for there can be no Idea of anything merely apparent: the general view is that an Idea is always spoken of in relation to an Idea: thus absolute desire is for the absolutely pleasant, and absolute wishing is for the absolutely good; they therefore cannot be for an apparent good or an apparently pleasant: for the existence of an absolutely-apparently-good or pleasant would be an absurdity.
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Moreover, if the definition be of the state of anything, look at what is in the state, while if it be of what is in the state, look at the state: and likewise also in other cases of the kind. Thus if the pleasant be identical with the beneficial, then, too, the man who is pleased is benefited. Speaking generally, in definitions of this sort it happens that what the definer defines is in a sense more than one thing: for in defining knowledge, a man in a sense defines ignorance as well, and likewise also what has 326
knowledge and what lacks it, and what it is to know and to be ignorant.
For if the first be made clear, the others become in a certain sense clear as well. We have, then, to be on our guard in all such cases against discrepancy, using the elementary principles drawn from consideration of contraries and of coordinates.
Moreover, in the case of relative terms, see if the species is rendered as relative to a species of that to which the genus is rendered as relative, e.g.
supposing belief to be relative to some object of belief, see whether a particular belief is made relative to some particular object of belief: and, if a multiple be relative to a fraction, see whether a particular multiple be made relative to a particular fraction. For if it be not so rendered, clearly a mistake has been made.
See, also, if the opposite of the term has the opposite definition, whether (e.g.) the definition of ‘half’ is the opposite of that of ‘double’: for if
‘double’ is ‘that which exceeds another by an equal amount to that other’, ‘half’ is ‘that which is exceeded by an amount equal to itself’. In the same way, too, with contraries. For to the contrary term will apply the definition that is contrary in some one of the ways in which contraries are
conjoined.
Thus
(e.g.)
if
‘useful’=’productive
of
good’,
‘injurious’=productive of evil’ or ‘destructive of good’, for one or the other of thee is bound to be contrary to the term originally used. Suppose, then, neither of these things to be the contrary of the term originally used, then clearly neither of the definitions rendered later could be the definition of the contrary of the term originally defined: and therefore the definition originally rendered of the original term has not been rightly rendered either. Seeing, moreover, that of contraries, the one is sometimes a word forced to denote the privation of the other, as (e.g.) inequality is generally held to be the privation of equality (for ‘unequal’
merely describes things that are not equal’), it is therefore clear that that contrary whose form denotes the privation must of necessity be defined through the other; whereas the other cannot then be defined through the one whose form denotes the privation; for else we should find that each is being interpreted by the other. We must in the case of contrary terms keep an eye on this mistake, e.g. supposing any one were to define equality as the contrary of inequality: for then he is defining it through the term which denotes privation of it. Moreover, a man who so defines is bound to use in his definition the very term he is defining; and this becomes clear, if for the word we substitute its definition. For to say
‘inequality’ is the same as to say ‘privation of equality’. Therefore equality so defined will be ‘the contrary of the privation of equality’, so that he 327
would have used the very word to be defined. Suppose, however, that neither of the contraries be so formed as to denote privation, but yet the definition of it be rendered in a manner like the above, e.g. suppose
‘good’ to be defined as ‘the contrary of evil’, then, since it is clear that
‘evil’ too will be ‘the contrary of good’ (for the definition of things that are contrary in this must be rendered in a like manner), the result again is that he uses the very term being defined: for ‘good’ is inherent in the definition of ‘evil’. If, then, ‘good’ be the contrary of evil, and evil be nothing other than the ‘contrary of good’, then ‘good’ will be the
‘contrary of the contrary of good’. Clearly, then, he has used the very word to be defined.
Moreover, see if in rendering a term formed to denote privation, he has failed to render the term of which it is the privation, e.g. the state, or contrary, or whatever it may be whose privation it is: also if he has omitted to add either any term at all in which the privation is naturally formed, or else that in which it is naturally formed primarily, e.g. whether in defining ‘ignorance’ a privation he has failed to say that it is the privation of ‘knowledge’; or has failed to add in what it is naturally formed, or, though he has added this, has failed to render the thing in which it is primarily formed, placing it (e.g.) in ‘man’ or in ‘the soul’, and not in the ‘reasoning faculty’: for if in any of these respects he fails, he has made a mistake. Likewise, also, if he has failed to say that ‘blindness’
is the ‘privation of sight in an eye’: for a proper rendering of its essence must state both of what it is the privation and what it is that is deprived.
Examine further whether he has defined by the expression ‘a privation’ a term that is not used to denote a privation: thus a mistake of this sort also would be generally thought to be incurred in the case of ‘error’
by any one who is not using it as a merely negative term. For what is generally thought to be in error is not that which has no knowledge, but rather that which has been deceived, and for this reason we do not talk of inanimate things or of children as ‘erring’. ‘Error’, then, is not used to denote a mere privation of knowledge.
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Moreover, see whether the like inflexions in the definition apply to the like inflexions of the term; e.g. if ‘beneficial’ means ‘productive of health’, does ‘beneficially’ mean productively of health’ and a
‘benefactor’ a ‘producer of health’?
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Look too and see whether the definition given will apply to the Idea as well. For in some cases it will not do so; e.g. in the Platonic definition where he adds the word ‘mortal’ in his definitions of living creatures: for the Idea (e.g. the absolute Man) is not mortal, so that the definition will not fit the Idea. So always wherever the words ‘capable of acting on’ or
‘capable of being acted upon’ are added, the definition and the Idea are absolutely bound to be discrepant: for those who assert the existence of Ideas hold that they are incapable of being acted upon, or of motion. In dealing with these people even arguments of this kind are useful.
Further, see if he has rendered a single common definition of terms that are used ambiguously. For terms whose definition corresponding their common name is one and the same, are synonymous; if, then, the definition applies in a like manner to the whole range of the ambiguous term, it is not true of any one of the objects described by the term. This is, moreover, what happens to Dionysius’ definition of ‘life’ when stated as
‘a movement of a creature sustained by nutriment, congenitally present with it’: for this is found in plants as much as in animals, whereas ‘life’ is generally understood to mean not one kind of thing only, but to be one thing in animals and another in plants. It is possible to hold the view that life is a synonymous term and is always used to describe one thing only, and therefore to render the definition in this way on purpose: or it may quite well happen that a man may see the ambiguous character of the word, and wish to render the definition of the one sense only, and yet fail to see that he has rendered a definition common to both senses instead of one peculiar to the sense he intends. In either case, whichever course he pursues, he is equally at fault. Since ambiguous terms sometimes pass unobserved, it is best in questioning to treat such terms as though they were s